Simplify the following expression: $p = \dfrac{6z^2 - 78z + 216}{z - 4} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $6$ , so we can rewrite the expression: $ p =\dfrac{6(z^2 - 13z + 36)}{z - 4} $ Then we factor the remaining polynomial: $z^2 {-13}z + {36} $ ${-4} {-9} = {-13}$ ${-4} \times {-9} = {36}$ $ (z {-4}) (z {-9}) $ This gives us a factored expression: $\dfrac{6(z {-4}) (z {-9})}{z - 4}$ We can divide the numerator and denominator by $(z + 4)$ on condition that $z \neq 4$ Therefore $p = 6(z - 9); z \neq 4$